Jenny, my Pyr, seems to have a nonexistent prey drive, but Tipper is a champion chaser and catcher of all critters! But he doesn't eat them, he just loves the chase. He has caught birds, bunnies, squirrels, and a raccoon. Squirrels are his personal favorite, however, one time after he caught the squirrel, the squirrel caught him--it had latched itself to Tipper's muzzle and wouldn't let go! Tipper was spinning around in circles trying to shake the thing off! It was quite a sight! But alas, it hasn't stopped him from chasing those squirrels, not even one little bit!
Your Jenny sounds like my full breed Pyrs are or have been. No prey drive at all.
Personally, I love it that way, I would hate to have some critter get eaten in my yard. Yeah, I know they are carnivores, but I just don't want it to happen here.
So, Pyrs work well for me in that regard. Cassie is probably 3/4 Pyr and the rest we just don't know, but whatever "it" is has some prey drive.
She will occasionally chase something, though I have never seen her catch anything, and I just hope that she doesn't.